Question

calcule a derivada da seguinte funcao f(x)=(x+3)/(x-1)

Answer 1

Explicação passo-a-passo:

Derivada

$\mathsf{F{(x)=\frac{a(x)}{b(x)}}}$

$\mathsf{F'{(x)=\frac{d}{dx}\frac{a'(x)\times b(x)-a(x)\times b'(x)}{{b(x)}^{2}}}}$

$\mathsf{F'{(x)=\frac{d}{dx}\frac{(X^{1-1}+{3}^{(1-1)})(x-1)-(x+3)(x^{1-1}-{1}^{(1-1)})}{{(x-1)}^{2}}}}$

$\mathsf{F'{(x)=\frac{1(x-1)-(x+3)1}{{(x-1)}^{2}}}}$

$\mathsf{F'{(x)=\frac{(x-1)-(x+3)}{{(x-1)}^{2}}}}$

$\mathsf{F'{(x)=\frac{x-1-x-3}{{(x-1)}^{2}}}}$

$\mathsf{F'{(x)=\frac{-4}{{(x-1)}^{2}}}}$

$\mathsf{\boxed{\boxed{F'{(x)=-\frac{4}{{(x-1)}^{2}}}}}}$